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@inbook{2392958, author = {Chajda, Ivan and Fazio, Davide and Länger, Helmut and Ledda, Antonio and Paseka, Jan}, address = {Cham}, booktitle = {Janusz Czelakowski on Logical Consequence}, doi = {http://dx.doi.org/10.1007/978-3-031-44490-6_15}, editor = {Malinowski, J., Palczewski, R.}, keywords = {Adjointness; Amalgam of Kleene lattices; Atomic amalgam; Kleene lattice; Kleene poset; Logics of quantum mechanics; Orthogonal poset; Orthomodular lattice; Orthomodular poset; Paraorthomodular poset; Relatively paraorthomodular poset; Sasaki implication}, howpublished = {tištěná verze "print"}, language = {eng}, location = {Cham}, isbn = {978-3-031-44489-0}, pages = {419-446}, publisher = {Springer}, title = {Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets}, url = {https://link.springer.com/chapter/10.1007/978-3-031-44490-6_15}, year = {2024} }
TY - CHAP ID - 2392958 AU - Chajda, Ivan - Fazio, Davide - Länger, Helmut - Ledda, Antonio - Paseka, Jan PY - 2024 TI - Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets VL - Outstanding Contributions to Logic, volume 27 PB - Springer CY - Cham SN - 9783031444890 KW - Adjointness KW - Amalgam of Kleene lattices KW - Atomic amalgam KW - Kleene lattice KW - Kleene poset KW - Logics of quantum mechanics KW - Orthogonal poset KW - Orthomodular lattice KW - Orthomodular poset KW - Paraorthomodular poset KW - Relatively paraorthomodular poset KW - Sasaki implication UR - https://link.springer.com/chapter/10.1007/978-3-031-44490-6_15 N2 - In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie’s theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices. ER -
CHAJDA, Ivan, Davide FAZIO, Helmut LÄNGER, Antonio LEDDA a Jan PASEKA. Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets. In Malinowski, J., Palczewski, R. \textit{Janusz Czelakowski on Logical Consequence}. Cham: Springer, 2024, s.~419-446. Outstanding Contributions to Logic, volume 27. ISBN~978-3-031-44489-0. Dostupné z: https://dx.doi.org/10.1007/978-3-031-44490-6\_{}15.
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